ERC FUNDED PROJECTS

The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods. Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject. We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small. We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration. Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further. Much of this is joint work with K Soundararajan of Stanford University.

2 011 742 €

Start date: 2015-08-01, End date: 2020-07-31

"Here, we propose a novel design for a significantly improved detector for the emerging field of coherent two-dimension infrared (2DIR) spectroscopy, which is an optical analog of Nuclear Magnetic Resonance spectroscopy (NMR). 2DIR is a cutting edge technique which is rapidly growing and has applications in subjects as diverse as energy sciences, biophysics, biomedical research and physical chemistry. Currently, the single most important technical problem that is generally agreed to limit applications of the methodology is the sensitivity with which the signals are measured. Having worked on multiple stabilisation techniques during the ERC funded research it was realised that a straightforward design alteration of the infrared detector will improve the sensitivity very significantly, theoretically by more than one order of magnitude. Here, the technical principles are explained, and a plan for commercialising the instrument in collaboration with the current market leader - Infrared System Development Corp. (ISDC) -. We apply for funding to develop the prototype."

149 999 €

Start date: 2013-11-01, End date: 2014-10-31

Darwin’s theory of natural selection rests on the principle that fitness variation in natural populations has a heritable component, on which selection acts, thereby leading to evolutionary change. A fundamental and so far unresolved question for the field of evolutionary biology is to identify the genetic loci responsible for this fitness variation, thereby coming closer to an understanding of how variation is maintained in the face of continual selection. One important complicating factor in the search for fitness related genes however is the existence of separate sexes – theoretical expectations and empirical data both suggest that sexually antagonistic genes are common. The phrase “two sexes, one genome” nicely sums up the problem; selection may favour alleles in one sex, even if they have detrimental effects on the fitness of the opposite sex, since it is their net effect across both sexes that determine the likelihood that alleles persist in a population. This theoretical framework raises an interesting, and so far entirely unexplored issue: that in one sex the functional performance of some alleles is predicted to be compromised and this effect may account for some common human diseases and conditions which show genotype-sex interactions. I propose to explore the genetic basis of sex-specific fitness in a model organism in both laboratory and natural conditions and to test whether those genes identified as having sexually antagonistic effects can help explain the incidence of human diseases that display sexual dimorphism in prevalence, age of onset or severity. This multidisciplinary project directly addresses some fundamental unresolved questions in evolutionary biology: the genetic basis and maintenance of fitness variation; the evolution of sexual dimorphism; and aims to provide novel insights into the genetic basis of some common human diseases.

1 500 000 €

Start date: 2012-01-01, End date: 2016-12-31

"This proposal develops a unified, underpinning technology to create novel, complex and biomimetic 3D environments for the control of tissue growth. As director of Cambridge Centre for Medical Materials, I have recently been approached by medical colleagues to help to solve important problems in the separate therapeutic areas of breast cancer, cardiac disease and blood disorders. In each case, the solution lies in complex 3D engineered environments for cell culture. These colleagues make it clear that existing 3D scaffolds fail to provide the required complex orientational and spatial anisotropy, and are limited in their ability to impart appropriate biochemical and mechanical cues. I have a strong track record in this area. A particular success has been the use of a freeze drying technology to make collagen based porous implants for the cartilage-bone interface in the knee, which has now been commercialised. The novelty of this proposal lies in the broadening of the established scientific base of this technology to enable biomacromolecular structures with: (A) controlled and complex pore orientation to mimic many normal multi-oriented tissue structures (B) compositional and positional control to match varying local biochemical environments, (C) the attachment of novel peptides designed to control cell behaviour, and (D) mechanical control at both a local and macroscopic level to provide mechanical cues for cells. These will be complemented by the development of (E) robust characterisation methodologies for the structures created. These advances will then be employed in each of the medical areas above. This approach is highly interdisciplinary. Existing working relationships with experts in each medical field will guarantee expertise and licensed facilities in the required biological disciplines. Funds for this proposal would therefore establish a rich hub of mutually beneficial research and opportunities for cross-disciplinary sharing of expertise."

2 486 267 €

Start date: 2013-04-01, End date: 2018-03-31